Related papers: Permanents through probability distributions

Several formulations have long existed in the literature in the form of continuous mixtures of normal variables where a mixing variable operates on the mean or on the variance or on both the mean and the variance of a multivariate normal…

We develop the theory of Wigner representations for general probabilistic theories (GPTs), a large class of operational theories that include both classical and quantum theory. The Wigner representations that we introduce are a natural way…

Fix a finite field $\mathbb F_q$ and let $A\in \mathbb F_q^{n\times n}$ be a uniformly random $n\times n$ matrix over $\mathbb F_q$. The asymptotic distribution of the determinant $\det(A)$ is well-understood, but the asymptotic…

From a transfer formula in multivariate finite operator calculus, comes an expansion for the determinant similar to Ryser's formula for the permanent. Although this one contains many more terms than the usual determinant formula. To prove…

We prove an identity relating the permanent of a rank $2$ matrix and the determinants of its Hadamard powers. When viewed in the right way, the resulting formula looks strikingly similar to an identity of Carlitz and Levine, suggesting the…

We give an introduction to some of the recent ideas that go under the name "geometric complexity theory". We first sketch the proof of the known upper and lower bounds for the determinantal complexity of the permanent. We then introduce the…

Drmota and Stufler proved recently that the expected number of pattern occurrences of a given map is asymptotically linear when the number of edges goes to infinity. In this paper we improve their result by means of a different method. Our…

We consider real symmetric or complex hermitian random matrices with correlated entries. We prove local laws for the resolvent and universality of the local eigenvalue statistics in the bulk of the spectrum. The correlations have fast decay…

In this paper we give the absolutely new proof of a conjecture of R.F.Scott(1881) on the permanent of a Cauchy matrix $\ls \frac{1}{x_i-y_j} \rs_{1 \leqslant i,j \leqslant n},$ where $x_1, ..., x_n$ and $y_1, ..., y_n$ are the distinct…

In this article we compute the number of invertible $2\times 2$ matrices with integer entries modulo $n$ whose permanents are congruent modulo $n$ to a given integer $x$.

We extend our generic rigidity theory for periodic frameworks in the plane to frameworks with a broader class of crystallographic symmetry. Along the way we introduce a new class of combinatorial matroids and associated linear…

We consider irreversible Markov chains on finite commutative rings randomly generated using both addition and multiplication. We restrict ourselves to the case where the addition is uniformly random and multiplication is arbitrary. We first…

We study the category Cstabm of measurable cones and measurable stable functions, which is a denotational model of an higher-order language with continuous probabilities and full recursion. We look at Cstabm as a model for discrete…

In the first part of this paper, we express the generalized Bessel function associated with dihedral systems and a constant multiplicity function as a infinite series of confluent Horn functions. The key ingredient leading to this…

Form an $n \times n$ matrix by drawing entries independently from $\{\pm1\}$ (or another fixed nontrivial finitely supported distribution in $\mathbf{Z}$) and let $\phi$ be the characteristic polynomial. Conditionally on the extended…

Taylor's theorem (and its variants) is widely used in several areas of mathematical analysis, including numerical analysis, functional analysis, and partial differential equations. This article explains how Taylor's theorem in its most…

Let $R$ be a commutative additively idempotent semiring. In this paper, some properties and characterizations for permanents of matrices over $R$ are established, and several inequalities for permanents are given. Also, the adjiont matrices…

We derive a generalization of the Perron-Frobenius theorem to time-varying row-stochastic matrices as follows: using Kolmogorov's concept of absolute probability sequences, which are time-varying analogs of principal eigenvectors, we…

Let $f:\mathbb{R}^k\to \mathbb{R}$ be a measurable function, and let $\{U_i\}_{i\in\mathbb{N}}$ be a sequence of i.i.d. random variables. Consider the random process $Z_i=f(U_{i},...,U_{i+k-1})$. We show that for all $\ell$, there is a…

A theorem of McCann shows that for any two absolutely continuous probability measures on R^d there exists a monotone transformation sending one probability measure to the other. A consequence of this theorem, relevant to statistics, is that…